Tomiyama-type maps with a diagonal perturbation

• URL: http://arxiv.org/abs/2604.18600v1
• Date: Thu, 09 Apr 2026 15:30:32 GMT
• Title: Tomiyama-type maps with a diagonal perturbation
• Abstract summary: We investigate a family of linear maps on matrix algebras constructed as diagonal perturbations of classical Tomiyama maps.<n>We derive explicit necessary and sufficient conditions for positivity, complete positivity, and k-positivity across arbitrary dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity techniques, we derive explicit necessary and sufficient conditions for positivity, complete positivity, and k-positivity across arbitrary dimensions. These conditions provide a transparent geometric characterization of the positivity regions within the parameter space.

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